first of all i doubt that there will be such war as i think people are evolved enough to not do that kind of stuff any more and no one will want for it to happen
though if it will happen nothing will survive it and if even bitcoin would survive it there wouldnt be anyone to use it, so i guess the answer would be that it wont survive it at all
not only bitcoin in all of sectors won't survive, peoples will not cares with such kind of that, in war situation they're just thinking about their safety and their life, the point is when the war is happened everything in this planet will be destroy including internet and bitcoin